The determination and refinement of heavy-atom parameters in protein heavy-atom derivatives. Some model calculations using acentric reflexions

Abstract

Some problems associated with the determination and refinement of heavy-atom parameters in protein derivatives using totally acentric data are critically examined with the aid of calculations on model systems. The difference Patterson (ΔF² Patterson) synthesis is found to be a good approximation to the heavy-atom vector map even when the substitution is high. A theoretical expansion for the coefficients of the conventional difference Fourier synthesis is given. The quality of the difference map decreases rapidly with increasing heavy-atom substitution. Theoretical considerations and model calculations show that the background noise closely resembles the features of the protein Fourier map. Statistical errors in the X-ray data are likely to lead to a systamatic overestimation of the occupancy factors when the heavy-atom parameters are refined by the least-squares method against the heavy-atom contributions estimated from isomorphous and anomalous differences. Refined occupancy factors reasonably, close to their true values can, however, be obtained either by using empirically evaluated values of k (the ratio between the real and imaginary parts of the heavy-atom form factor) in estimating the heavy-atom contribution or by applying suitable weighting functions to the terms in the minimization function. Some aspects of the least-squares method based on tbe minimization of the sum of squares of the lack-of-closure errors are also discussed.